MAS241 Mathematics II (Electrical)
|Semester 1, 2021/22||10 Credits|
|Lecturer:||Prof Vladimir Bavula||Timetable||Reading List|
Prerequisites: MAS156 (Mathematics (Electrical and Aerospace))
The following modules have this module as a prerequisite:
|MAS381||Mathematics III (Electrical)|
- To consolidate previous mathematical knowledge.
- To develop the mathematical techniques used in second year electrical and aeronautical engineering courses.
- To lay the foundations for the study of vector calculus.
- Ability to understand complex valued functions, and functions of a complex variable.
- Ability to compute Laplace and Fourier transforms and apply the Laplace transform to solve differential equations.
- Ability to compute Fourier series, and Fourier sine and cosine series.
- Ability to find partial and directional derivatives.
- Ability to apply the chain rule to functions of multiple variables.
- Ability to find critical points of a function of two variables and determine their nature.
- Ability to compute double and triple integrals directly and/or by changing the order of integration/changing variables.
- Ability to compute the gradient of a scalar field, understand and apply its geometric interpretation.
- Ability to compute divergence and curl of a vector field.
22 lectures, 11 tutorials
One formal 2 hour written examination.
- Review of complex numbers and complex valued functions
- Important real valued functions including the Heaviside, unit impluse and delta functions; complex Laplace transform and its properties; convolution; applications of the Laplace transform; the Fourier transform and its properties.
- Fourier series
- Periodic functions; Fourier series; even and odd functions; Fourier cosine and sine series; complex exponential Fourier series.
- Functions of several variables
- Review of partial derivatives; directional derivatives; chain rule; gradient vector and its geometric interpretation; higher order derivatives and equality of mixed derivatives; determining the nature of critical points for functions of two variables.
- The definite integral; double and triple integrals, their geometric interpretations and properties; change of order of integration; change of variables; surface areas; cylindrical and spherical polar coordinates.
- Vector fields
- Vector and scalar fields; divergence and curl; elementary properties of divergence and curl.
|B||Dennis Zill, Warren Wright||Advanced Engineering Mathematics|
|B||Robert Adams||Calculus: A Complete Course|
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop at Jessop West.